Complex numbers: i, adding, multiplying, dividing
Meet the number i with i² = −1, add complex numbers as points on the plane, multiply them like brackets and divide with the conjugate.
- UK: Year 12
- France: grade 12
- Afghanistan: grade 10
- Syria: grade 12
- Palestine: grade 12
- Russia: grade 11
Guide
The imaginary unit is i, with i2 = −1. A complex number is written a + bi: a is the real part and b is the imaginary part. On the complex plane the real part goes across and the imaginary part goes up, so 2 + 3i is the point 2 across and 3 up.
To add, add the real parts and add the imaginary parts. To multiply, expand the brackets, then replace i2 by −1.
To divide, multiply the top and the bottom by the conjugate of the bottom. The conjugate of a + bi is a − bi, and (a + bi)(a − bi) = a2 + b2 is a real number.